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Abdou Abdel-Rehim

Publications and source records attributed to Abdou Abdel-Rehim.

16 recordsLinked to original sources
arXiv2017

Investigating efficient methods for computing four-quark correlation functions

We discuss and compare the efficiency of various methods, combinations of point-to-all propagators, stochastic timeslice-to-all propagators, the one-end trick and sequential propagators, to compute two-point correlation functions of two-quark and four-quark interpolating operators of different structure including quark-antiquark type, mesonic molecule type, diquark-antidiquark type and two-meson type. Although we illustrate our methods in the context of the $a_0(980)$, they can be applied for other multi-quark systems, where similar diagrams appear. Thus our results could provide helpful guidelines on the choice of methods for correlation function computation for future lattice QCD studies of meson-meson scattering and possibly existing tetraquark states.

hep-lat↗
arXiv2016

Importance of closed quark loops for lattice QCD studies of tetraquarks

To investigate the light scalar tetraquark candidate $a_0(980)$ (quantum numbers $J^P =0^+$), a correlation matrix including a variety of two- and four-quark interpolating operators has to be computed. We discuss efficient techniques to compute the elements of this correlation matrix, in particular diagrams with closed quark loops. Furthermore, we present evidence that such diagrams are not negligible given our precision, and their contribution is essential to obtain physically meaningful results. In particular, we find indications of the existence of an "additional" state around the two-particle thresholds of $K+ \bar K$ and $η+π$, which could correspond to the $a_0(980)$ meson.

hep-lat↗
arXiv2016

Disconnected diagrams with twisted-mass fermions

The latest results from the Twisted-Mass collaboration on disconnected diagrams at the physical value of the pion mass are presented. In particular, we focus on the sigma terms, the axial charges and the momentum fraction, all of them for the nucleon. A detailed error analysis for each observable follows, showing the strengths and weaknesses of the one-end trick. Alternatives are discussed.

hep-lat↗
arXiv2015

Computation of correlation matrices for tetraquark candidates with $J^P = 0^+$ and flavor structure $q_1 \bar{q_2} q_3 \bar{q}_3$

The conjecture that several recently observed mesons have a structure, which is not dominated by an ordinary quark-antiquark pair, but by a four-quark structure, is being actively investigated both theoretical and experimentally. Such a state may be characterized as a mesonic molecule or as a diquark-antidiquark pair. Lattice QCD provides a theoretically sound framework to study such states. To quantitatively investigate the internal structure of such mesons, one needs to precisely compute correlation matrices containing several interpolating operators including two and four quarks. Here we discuss certain technical aspects of such correlation matrices suited to study tetraquark candidates with $J^P = 0^+$ and flavor structure $q_1 \bar{q_2} q_3 \bar{q}_3$, e.g.\ the $a_0(980)$ meson, the $D_{s0}^\ast$ meson and some of the charged $c \bar{c}$ $X$ states. Some numerical results for the $a_0(980)$ meson are presented.

hep-lat↗
arXiv2015

Nucleon electromagnetic form factors from twisted mass lattice QCD

Results on the electromagnetic form factors of the nucleon using twisted mass fermion configurations are presented. These include a gauge field ensemble simulated with two degenerate light quarks yielding a pion mass of around 130 MeV, as well as two ensembles that include strange and charm quarks in the sea yielding pion masses of 210 MeV and 373 MeV. Details of the methods used and systematic errors are discussed, such as noise reduction techniques and the effect of excited states contamination.

hep-lat↗
arXiv2014

Investigation of the tetraquark candidate $a_0(980)$: technical aspects and preliminary results

We discuss technical aspects and first results of a lattice QCD study of the $a_0(980)$ state. We employ various interpolating operators of quark-antiquark, mesonic molecule, diquark-antidiquark and two-meson type. Both connected and disconnected contributions including diagrams with closed fermion loops are computed. To keep statistical errors small, it is essential to optimize the computation of these diagrams by choosing that combination of techniques most appropriate for each type of diagram from the correlation matrix of interpolating operators. We illustrate, how this can be done, by discussing certain diagrams in detail. We also present preliminary results corresponding to a $4\times 4$ submatrix computed with 2+1 flavors of clover fermions.

hep-lat↗
arXiv2013

Recent developments in the tmLQCD software suite

We present an overview of recent developments in the tmLQCD software suite. We summarise the features of the code, including actions and operators implemented. In particular, we discuss the optimisation efforts for modern architectures using the Blue Gene/Q system as an example.

hep-lat↗
arXiv2013

Study of the a_0(980) on the lattice

We present lattice results for the a_0(980) state using a variational approach with a variety of creation operators: quark-antiquark, mesonic molecule, diquark-antidiquark as well as two-meson type. Focus is put on recent technical advances, in particular the computation of singly disconnected diagrams.

hep-lat↗
arXiv2011

Application of Quadrature Methods for Re-Weighting in Lattice QCD

Re-weighting is a useful tool that has been employed in Lattice QCD in different contexts including, tuning the strange quark mass, approaching the light quark mass regime, and simulating electromagnetic fields on top of QCD gauge configurations. In case of re-weighting the sea quark mass, the re-weighting factor is given by the ratio of the determinants of two Dirac operators $D_a$ and $D_b$. A popular approach for computing this ratio is to use a pseudofermion representation of the determinant of the composite operator $Ω=D_a(D_b^\dagger D_b)^{-1} D_a^\dagger$. Here, we study using quadrature methods together with noise vectors to compute the ratio of determinants. We show that, with quadrature methods each determinant can be computed separately using the operators $Ω_a=D_a^\dagger D_a$ and $Ω_b=D_b^\dagger D_b$. We also discuss using bootstrap re-sampling to remove the bias from the determinant estimator.

hep-lat↗
arXiv2009

Extending the eigCG algorithm to non-symmetric linear systems with multiple right-hand sides

For Hermitian positive definite linear systems and eigenvalue problems, the eigCG algorithm is a memory efficient algorithm that solves the linear system and simultaneously computes some of its eigenvalues. The algorithm is based on the Conjugate-Gradient (CG) algorithm, however, it uses only a window of the vectors generated by the CG algorithm to compute approximate eigenvalues. The number and accuracy of the eigenvectors can be increased by solving more right-hand sides. For Hermitian systems with multiple right-hand sides, the computed eigenvectors can be used to speed up the solution of subsequent systems. The algorithm was tested on Lattice QCD problems by solving the normal equations and was shown to give large speed up factors and to remove the critical slowing down as we approach light quark masses. Here, an extension to the non-symmetric case based on the two-sided Lanczos algorithm is given. The new algorithm is tested on Lattice QCD problems and is shown to give promising results. We also study the removal of the critical slowing down and compare results with those of the eigCG algorithm. We also discuss the case when the system is gamma5-Hermitian.

hep-lat↗
arXiv2009

Seed methods for linear equations in lattice qcd problems with multiple right-hand sides

We consider three improvements to seed methods for Hermitian linear systems with multiple right-hand sides: only the Krylov subspace for the first system is used for seeding subsequent right-hand sides, the first right-hand side is solved past convergence, and periodic re-orthogonalization is used in order to control roundoff errors associated with the Conjugate Gradient algorithm. The method is tested for the case of Wilson fermions near kappa critical and a considerable speed up in the convergence is observed.

hep-lat↗
arXiv2007

Vacuum Expectation Values of Twisted Mass Fermion Operators

Using noise methods on a quenched $20^3 \times 32$ lattice at $β=6.0$, we have investigated vacuum expectation values and relative linear correlations among the various Wilson and twisted mass scalar and pseudoscalar disconnected loop operators. We show results near the maximal twist lines in $κ$, $μ$ parameter space, either defined as the absence of parity mixing or the vanishing of the PCAC quark mass.

hep-lat↗
arXiv2007

Deflated BiCGStab for linear equations in QCD problems

The large systems of complex linear equations that are generated in QCD problems often have multiple right-hand sides (for multiple sources) and multiple shifts (for multiple masses). Deflated GMRES methods have previously been developed for solving multiple right-hand sides. Eigenvectors are generated during solution of the first right-hand side and used to speed up convergence for the other right-hand sides. Here we discuss deflating non-restarted methods such as BiCGStab. For effective deflation, both left and right eigenvectors are needed. Fortunately, with the Wilson matrix, left eigenvectors can be derived from the right eigenvectors. We demonstrate for difficult problems with kappa near kappa_c that deflating eigenvalues can significantly improve BiCGStab. We also will look at improving solution of twisted mass problems with multiple shifts. Projecting over previous solutions is an easy way to reduce the work needed.

hep-lat↗
arXiv2003

Comparing the Higgs Sector of Electroweak Theory with the Scalar Sector of Low Energy QCD

We first review how the simple K-matrix unitarized linear SU(2) sigma model can explain the experimental data in the scalar pi pi scattering channel of QCD up to about 800 MeV. Since it is just a scaled version of the minimal electroweak Higgs sector, which is often treated with the same unitarization method, we interpret the result as support for this approach in the electroweak model with scaled values of tree level Higgs mass up to at least about 2 TeV. We further note that the relevant QCD effective Lagrangian which fits the data to still higher energies using the same method involves another scalar resonance. This suggests that the method should also be applicable to corresponding beyond minimal electroweak models. Nevertheless we note that even with one resonance, the minimal K matrix unitarized model behaves smoothly for large bare Higgs mass by effectively "integrating out" the Higgs while preserving unitarity. With added confidence in this simple approach we make a survey of the Higgs sector for the full range of bare Higgs mass. One amusing point which emerges is that the characteristic factor of the W-W fusion mechanism for Higgs production peaks at the bare mass of the Higgs boson, while the characteristic factor for the gluon fusion mechanism peaks near the generally lower physical mass.

hep-ph↗